Interest Rates, Corporate Bonds, and Mortgage-Backed Securities

A corporate treasurer prices a 10-year fixed-rate note at 5.5% yield to maturity (YTM) and the same maturity Treasury at 4.2%. The 130 bp spread compensates for default and liquidity. A pension fund buys a $50 million mortgage-backed security (MBS) pool yielding 5.8%, knowing the homeowners can refinance and hand back capital just when rates fall the most. The exam tests whether you can move between rate conventions, price duration and convexity correctly, decompose a corporate bond's spread, and understand why prepayment risk wrecks naive bond math on MBS.

The reference rate landscape changed materially after LIBOR's retirement. Secured Overnight Financing Rate (SOFR) (Secured Overnight Financing Rate) is now the dominant USD risk-free benchmark. It is collateralized by Treasury repo, calculated daily, and replaces LIBOR in most new derivatives.

Treasury rates, SOFR, and repo rates are all candidates for the "risk-free" rate in pricing models. Each has trade-offs. Treasuries have the deepest liquidity but reflect a mild scarcity premium. SOFR is overnight and derivative-friendly but lacks a historical term structure.

Common mistakes

• Confusing Macaulay and modified duration. Macaulay is in years (weighted-average time). Modified is the price sensitivity (percent per yield bp). They differ by the factor 1 + y/m. Trap: a question gives Macaulay 7.5 years and asks "% price change for a 50 bp rate rise." Wrong answer: 7.5 × 0.005 = 3.75%.
• Plugging semi-annual YTM into a continuous discount. A 6% YTM on a U.S. corporate is semi-annual; PV is $\sum C{F}_t/(1.03{)}^{2t}$. Plugging into $e^{-0.06t}$ gives a different number. Trap: continuous-time models (Black-Scholes for bond options, FRM derivative chapters) need the rate converted first.
• Using duration alone for large rate moves. A 200 bp rate move on a 7-year duration bond: duration says -14% but actual move might be -12% due to positive convexity. Trap: question gives a 200 bp shock and asks for the price change.

Bottom line

• Compounding conversion: $R_c=m\ln (1+R_m/m)$. Continuous and discrete give the same PV but different rate quotes.
• Duration: Macaulay (years), Modified = Mac / (1 + y/m) (percent-per-bp), Dollar = Modified × Price (dollars-per-bp). $\Delta P/P\approx -D_{\text{mod}}\Delta y$.
• Convexity: the second-order term improving the linear estimate, $\Delta P/P\approx -D\Delta y+\frac{1}{2}C(\Delta y{)}^2$; positive for vanilla bonds, negative for callable bonds and MBS.
• Term structure theories: pure expectations, liquidity preference (term premium), market segmentation, preferred habitat.

Exam shortcut

When a duration question lands, ask: is the rate move small (≤25 bp) and the bond vanilla? Use modified duration alone. Larger move or callable / MBS? Add convexity. The trap is using nominal duration on an MBS, since the prepayment option flips convexity negative below a refi rate threshold.

The full lesson (about 3,337 words, 22 min read) adds 2 worked examples, all 6 common mistakes, a self-check, free in the app.

Learning objectives

• 1
• 2
• 3
• 4
• 5
• 6
• 7
• 8
• 9
• 10
• 11
• 12
• 13
• 14
• 15
• 16
• 17
• 18
• 19
• 20

Browse all free FRM Part I lessons or jump into free FRM Part I practice questions.